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arXiv · 2512.04607

Mode interactions in scalar field cosmology

Spiros Cotsakis·Ignatios Antoniadis
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Abstract

We study the dynamics of spatially homogeneous Friedmann--Robertson--Walker universes filled with a massive scalar field in a neighbourhood of the massless transition $s=1$. At this point the Einstein--scalar system exhibits a codimension--two Hopf--steady--state organising centre whose versal unfolding describes all small deformations of the quadratic model. After reduction to the centre manifold, the dynamics is governed by two slow geometric modes $(r,z)$: the Hopf amplitude $r$, measuring the kinetic departure from de Sitter, and the slowly drifting Hubble mode $z$. We show that the standard slow--roll parameters follow directly from these unfolding variables, $\epsilon\sim\tfrac32 r^{2}$ and $\eta\sim z$, so that the spectral tilt, tensor--to--scalar ratio, and scalar amplitude arise as universal functions of $(r,z)$, independently of the choice of potential. The two unfolding parameters $(\mu_{1},\mu_{2})$ classify all perturbations of the quadratic model and can be interpreted physically as controlling the tilt and curvature deformations of generic polynomial inflationary potentials. Thus the near scale--invariance of primordial perturbations emerges as a structural property of the unfolding of the organising centre, providing a potential--independent mechanism for an early phase of accelerated expansion. We discuss the implications of this geometric framework for the interpretation and classification of inflationary models.

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Spiros Cotsakis, Ignatios Antoniadis. 2025-12-04. Mode interactions in scalar field cosmology. https://arxiv.org/abs/2512.04607

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